Problem 24 - Chemistry for Allied Health

Question

Perform the indicated conversions for the following pressure measurements. a. \(1.721\) atm to \(\mathrm{mmHg}\) b. 559 torr to \(\mathrm{kPa}\) c. \(91.1 \mathrm{kPa}\) to atm d. \(2320 \mathrm{mmHg}\) to atm

Step-by-Step Solution

Answer

a. 1307.96 mmHg, b. 74.52 kPa, c. 0.899 atm, d. 3.053 atm.

Step 1: Understand Conversion Units

To solve these pressure conversions, we need to know the conversion factors between the units: 1. 1 atm = 760 mmHg 2. 1 atm = 101.325 kPa 3. 1 mmHg = 1 torr. These factors will help you convert from one unit to another.

Step 2a: Convert 1.721 atm to mmHg

Multiply the pressure in atmospheres by the number of mmHg per atmosphere:\[1.721 \, \text{atm} \times 760 \, \frac{\text{mmHg}}{\text{atm}} = 1307.96 \, \text{mmHg}\]

Step 2b: Convert 559 torr to kPa

Since 1 mmHg (torr) = 1 atm / 760, first convert torr to atm, then to kPa:\[559 \, \text{torr} = \frac{559}{760} \, \text{atm} \approx 0.7355 \, \text{atm}\]Now convert atm to kPa:\[0.7355 \, \text{atm} \times 101.325 \, \frac{\text{kPa}}{\text{atm}} \approx 74.52 \, \text{kPa}\]

Step 2c: Convert 91.1 kPa to atm

Use the conversion factor from kPa to atm:\[91.1 \, \text{kPa} \times \frac{1 \, \text{atm}}{101.325 \, \text{kPa}} \approx 0.899 \, \text{atm}\]

Step 2d: Convert 2320 mmHg to atm

Since 1 atm = 760 mmHg, divide the pressure by 760 to convert to atm:\[2320 \, \text{mmHg} \times \frac{1 \, \text{atm}}{760 \, \text{mmHg}} \approx 3.053 \, \text{atm}\]

Key Concepts

Atmospheres to mmHg

Converting atmospheres to millimeters of mercury (mmHg) is a common task in chemistry, especially when working with pressures in experiments. The conversion is straightforward once you remember the key relationship: 1 atmosphere (atm) is equivalent to 760 mmHg.
To convert a given pressure from atmospheres to mmHg, simply multiply the value in atmospheres by 760. For example, if you need to convert 1.721 atm to mmHg, you perform the following calculation:

• Multiply:
  • 1.721 atm
  - 760 mmHg/atm
• Result:
  • 1307.96 mmHg
  This easy conversion helps to ensure precise measurements and calculations in various science-related fields.

Torr to kPa Conversion

The conversion from torr to kilopascals (kPa) involves a couple of straightforward steps. You start by remembering that 1 mmHg (which is equal to 1 torr) is equivalent to \(\frac{1}{760}\) atm. Once you convert torr to atmospheres, you can then convert to kPa.
To convert 559 torr to kPa, follow these steps:

• First, convert torr to atmospheres:
  • \(559 \, \text{torr} = \frac{559}{760} \, \text{atm} \approx 0.7355 \, \text{atm}\)
• Next, convert atmospheres to kPa using the conversion factor 1 atm = 101.325 kPa:
  • \(0.7355 \, \text{atm} \times 101.325 \, \frac{\text{kPa}}{\text{atm}} \approx 74.52 \, \text{kPa}\)

With this method, you ensure accuracy and consistency in your pressure conversions.

kPa to Atmospheres

Converting kilopascals (kPa) to atmospheres is a vital skill, especially in fields like physics and chemistry where pressure measurements vary widely. The conversion is straightforward due to the direct relationship between these units: 1 atmosphere is equivalent to 101.325 kPa.
To convert a pressure measurement from kPa to atmospheres, you divide the value in kPa by 101.325. For instance, if you're converting 91.1 kPa to atmospheres, you compute:

• Divide:
  • \(91.1 \, \text{kPa} \times \frac{1 \, \text{atm}}{101.325 \, \text{kPa}} \approx 0.899 \, \text{atm}\)
  This conversion method ensures that your pressure values remain accurate and reliable across different units of measurement.

mmHg to Atmospheres

When converting from mmHg to atmospheres, it's essential to remember the key conversion factor: 1 atmosphere is equivalent to 760 mmHg. This relationship allows you to easily convert pressure measurements from one unit to the other.
For example, to convert 2320 mmHg to atmospheres, simply divide the mmHg value by 760:

• Divide:
  • \(2320 \, \text{mmHg} \times \frac{1 \, \text{atm}}{760 \, \text{mmHg}} \approx 3.053 \, \text{atm}\)
  By using this conversion factor, you can ensure your calculations remain precise and accurate, no matter the pressure units you're dealing with.